# Digital Signal Processing: Principles, Algorithms, and Applications, 5th edition

## Digital Signal Processing (Subscription)

ISBN-13: 9780137376063

### What's included

## Overview

** Digital Signal Processing** presents the fundamental concepts and techniques of discrete-time signals, systems, and modern digital processing as well as related algorithms and applications for students in electrical engineering, computer engineering, and computer science departments.

Covering both time-domain and frequency-domain methods for the analysis of linear, discrete-time systems, the** 5th Edition** includes a new chapter on multirate digital filter banks and wavelets. Several new topics have been added to existing chapters, including the short-time Fourier Transform, the sparse FFT algorithm, ARMA model parameter estimation, and reverberation filters. Rigorous and challenging, it includes numerous examples and over 500 homework and computer problems that emphasize software implementation of digital signal processing algorithms.

## Table of contents

**1. ****Introduction **

1.1 Signals, Systems, and Signal Processing

1.1.1 Basic Elements of a Digital Signal Processing System

1.1.2 Advantages of Digital over Analog Signal Processing

1.2 Classification of Signals

1.2.1 Multichannel and Multidimensional Signals

1.2.2 Continuous-Time Versus Discrete-Time Signals

1.2.3 Continuous-Valued Versus Discrete-Valued Signals

1.2.4 Deterministic Versus Random Signals

1.3 Summary

Problems

**2. Discrete-Time Signals and Systems **2.1 Discrete-Time Signals

2.1.1 Some Elementary Discrete-Time Signals

2.1.2 Classification of Discrete-Time Signals

2.1.3 Simple Manipulations of Discrete-Time Signals

2.2 Discrete-Time Systems

2.2.1 Input-Output Description of Systems

2.2.2 Block Diagram Representation of Discrete-Time Systems

2.2.3 Classification of Discrete-Time Systems

2.2.4 Interconnection of Discrete-Time Systems

2.3 Analysis of Discrete-Time Linear Time-Invariant Systems

2.3.1 Techniques for the Analysis of Linear Systems

2.3.2 Resolution of a Discrete-Time Signal into Impulses

2.3.3 Response of LTI Systems to Arbitrary Inputs: The Convolution Sum

2.3.4 Properties of Convolution and the Interconnection of LTI Systems

2.3.5 Causal Linear Time-Invariant Systems

2.3.6 Stability of Linear Time-Invariant Systems

2.3.7 Systems with Finite-Duration and Infinite-Duration Impulse Response

2.4 Discrete-Time Systems Described by Difference Equations

2.4.1 Recursive and Nonrecursive Discrete-Time Systems

2.4.2 Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations

2.4.3 Application of LTI Systems for Signal Smoothing

2.5 Implementation of Discrete-Time Systems

2.5.1 Structures for the Realization of Linear Time-Invariant Systems

2.5.2 Recursive and Nonrecursive Realizations of FIR Systems

2.6 Correlation of Discrete-Time Signals

2.6.1 Crosscorrelation and Autocorrelation Sequences

2.6.2 Properties of the Autocorrelation and Crosscorrelation Sequences

2.6.3 Correlation of Periodic Sequences

2.6.4 Input-Output Correlation Sequences

2.7 Summary

Problems

Computer Problems

**3****.****The z-Transform and Its Application to the Analysis of LTI ****Systems **3.1 The z-Transform

3.1.1 The Direct z-Transform

3.1.2 The Inverse z-Transform

3.2 Properties of the z-Transform

3.3 Rational z-Transforms

3.3.1 Poles and Zeros

3.3.2 Pole Location and Time-Domain Behavior for Causal Signals

3.3.3 The System Function of a Linear Time-Invariant System

3.4 Inversion of the z-Transform

3.4.1 The Inverse z-Transform by Contour Integration

3.4.2 The Inverse z-Transform by Power Series Expansion

3.4.3 The Inverse z-Transform by Partial-Fraction Expansion

3.4.4 Decomposition of Rational z-Transforms

3.5 Analysis of Linear Time-Invariant Systems in the z-Domain

3.5.1 Response of Systems with Rational System Functions

3.5.2 Transient and Steady-State Responses

3.5.3 Causality and Stability

3.5.4 Pole–Zero Cancellations

3.5.5 Multiple-Order Poles and Stability

3.5.6 Stability of Second-Order Systems

3.6 The One-sided z-Transform

3.6.1 Definition and Properties

3.6.2 Solution of Difference Equations

3.6.3 Response of Pole–Zero Systems with Nonzero Initial Conditions

3.7 Summary

Problems

Computer Problems

**4****. ****Frequency Analysis of Signals **4.1 The Concept of Frequency in Continuous-Time and Discrete-Time Signals

4.1.1 Continuous-Time Sinusoidal Signals

4.1.2 Discrete-Time Sinusoidal Signals

4.1.3 Harmonically Related Complex Exponentials

4.1.4 Sampling of Analog Signals

4.1.5 The Sampling Theorem

4.2 Frequency Analysis of Continuous-Time Signals

4.2.1 The Fourier Series for Continuous-Time Periodic Signals

4.2.2 Power Density Spectrum of Periodic Signals

4.2.3 The Fourier Transform for Continuous-Time Aperiodic Signals

4.2.4 Energy Density Spectrum of Aperiodic Signals

4.3 Frequency Analysis of Discrete-Time Signals

4.3.1 The Fourier Series for Discrete-Time Periodic Signals

4.3.2 Power Density Spectrum of Periodic Signals

4.3.3 The Fourier Transform of Discrete-Time Aperiodic Signals

4.3.4 Convergence of the Fourier Transform

4.3.5 Energy Density Spectrum of Aperiodic Signals

4.3.6 Relationship of the Fourier Transform to the z-Transform

4.3.7 The Cepstrum

4.3.8 The Fourier Transform of Signals with Poles on the Unit Circle

4.3.9 Frequency-Domain Classification of Signals: The Concept of Bandwidth

4.3.10 The Frequency Ranges of Some Natural Signals

4.4 Frequency-Domain and Time-Domain Signal Properties

4.5 Properties of the Fourier Transform for Discrete-Time Signals

4.5.1 Symmetry Properties of the Fourier Transform

4.5.2 Fourier Transform Theorems and Properties

4.6 Summary

Problems

Computer Problems

**5****. ****Frequency-Domain Analysis of LTI Systems **5.1 Frequency-Domain Characteristics of Linear Time-Invariant Systems

5.1.1 Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function

5.1.2 Steady-State and Transient Response to Sinusoidal Input Signals

5.1.3 Steady-State Response to Periodic Input Signals

5.1.4 Steady-State Response to Aperiodic Input Signals

5.2 Frequency Response of LTI Systems

5.2.1 Frequency Response of a System with a Rational System Function

5.2.2 Computation of the Frequency Response Function

5.3 Correlation Functions and Spectra at the Output of LTI Systems

5.4 Linear Time-Invariant Systems as Frequency-Selective Filters

5.4.1 Ideal Filter Characteristics

5.4.2 Lowpass, Highpass, and Bandpass Filters

5.4.3 Digital Resonators

5.4.4 Notch Filters

5.4.5 Comb Filters

5.4.6 Reverberation Filters

5.4.7 All-Pass Filters

5.4.8 Digital Sinusoidal Oscillators

5.5 Inverse Systems and Deconvolution

5.5.1 Invertibility of Linear Time-Invariant Systems

5.5.2 Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems

5.5.3 System Identification and Deconvolution

5.5.4 Homomorphic Deconvolution

5.6 Summary

Problems

Computer Problems

**6****. ****Sampling and Reconstruction of Signals **6.1 Ideal Sampling and Reconstruction of Continuous-Time Signals

6.2 Discrete-Time Processing of Continuous-Time Signals

6.3 Sampling and Reconstruction of Continuous-Time Bandpass Signals

6.3.1 Uniform or First-Order Sampling

6.3.2 Interleaved or Nonuniform Second-Order Sampling

6.3.3 Bandpass Signal Representations

6.3.4 Sampling Using Bandpass Signal Representations

6.4 Sampling of Discrete-Time Signals

6.4.1 Sampling and Interpolation of Discrete-Time Signals

6.4.2 Representation and Sampling of Bandpass Discrete-Time Signals

6.5 Analog-to-Digital and Digital-to-Analog Converters

6.5.1 Analog-to-Digital Converters

6.5.2 Quantization and Coding

6.5.3 Analysis of Quantization Errors

6.5.4 Digital-to-Analog Converters

6.6 Oversampling A/D and D/A Converters

6.6.1 Oversampling A/D Converters

6.6.2 Oversampling D/A Converters

6.7 Summary

Problems

Computer Problems

**7****. ****The Discrete Fourier Transform: Its Properties****and Applications **7.1 Frequency-Domain Sampling: The Discrete Fourier Transform

7.1.1 Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals

7.1.2 The Discrete Fourier Transform (DFT)

7.1.3 The DFT as a Linear Transformation

7.1.4 Relationship of the DFT to Other Transforms

7.2 Properties of the DFT

7.2.1 Periodicity, Linearity, and Symmetry Properties

7.2.2 Multiplication of Two DFTs and Circular Convolution

7.2.3 Additional DFT Properties

7.3 Linear Filtering Methods Based on the DFT

7.3.1 Use of the DFT in Linear Filtering

7.3.2 Filtering of Long Data Sequences

7.4 Frequency Analysis of Signals Using the DFT

7.5 The Short-Time Fourier Transform

7.6 The Discrete Cosine Transform

7.6.1 Forward DCT

7.6.2 Inverse DCT

7.6.3 DCT as an Orthogonal Transform

7.7 Summary

Problems

Computer Problems

**8****. ****Efficient Computation of the DFT: Fast Fourier Transform ****Algorithms **8.1 Efficient Computation of the DFT: FFT Algorithms

8.1.1 Direct Computation of the DFT

8.1.2 Divide-and-Conquer Approach to Computation of the DFT

8.1.3 Radix-2 FFT Algorithms

8.1.4 Radix-4 FFT Algorithms

8.1.5 Split-Radix FFT Algorithms

8.1.6 Implementation of FFT Algorithms

8.1.7 Sparse FFT Algorithm

8.2 Applications of FFT Algorithms

8.2.1 Efficient Computation of the DFT of Two Real Sequences

8.2.2 Efficient Computation of the DFT of a 2N-Point Real Sequence

8.2.3 Use of the FFT Algorithm in Linear Filtering and Correlation

8.3 A Linear Filtering Approach to Computation of the DFT

8.3.1 The Goertzel Algorithm

8.3.2 The Chirp-z Transform Algorithm

8.4 Quantization Effects in the Computation of the DFT

8.4.1 Quantization Errors in the Direct Computation of the DFT

8.4.2 Quantization Errors in FFT Algorithms

8.5 Summary

Problems

Computer Problems

**9****. ****Implementation of Discrete-Time Systems **9.1 Structures for the Realization of Discrete-Time Systems

9.2 Structures for FIR Systems

9.2.1 Direct-Form Structure

9.2.2 Cascade-Form Structures

9.2.3 Frequency-Sampling Structures

9.2.4 Lattice Structure

9.3 Structures for IIR Systems

9.3.1 Direct-Form Structures

9.3.2 Signal Flow Graphs and Transposed Structures

9.3.3 Cascade-Form Structures

9.3.4 Parallel-Form Structures

9.3.5 Lattice and Lattice-Ladder Structures for IIR Systems

9.4 Representation of Numbers

9.4.1 Fixed-Point Representation of Numbers

9.4.2 Binary Floating-Point Representation of Numbers

9.4.3 Errors Resulting from Rounding and Truncation

9.5 Quantization of Filter Coefficients

9.5.1 Analysis of Sensitivity to Quantization of Filter Coefficients

9.5.2 Quantization of Coefficients in FIR Filters

9.6 Round-Off Effects in Digital Filters

9.6.1 Limit-Cycle Oscillations in Recursive Systems

9.6.2 Scaling to Prevent Overflow

9.6.3 Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters

9.7 Summary

Problems

Computer Problems

**10****. ****Design of Digital Filters **10.1 General Considerations

10.1.1 Causality and Its Implications

10.1.2 Characteristics of Practical Frequency-Selective Filters

10.2 Design of FIR Filters

10.2.1 Symmetric and Antisymmetric FIR Filters

10.2.2 Design of Linear-Phase FIR Filters Using Windows

10.2.3 Design of Linear-Phase FIR Filters by the Frequency-Sampling Method

10.2.4 Design of Optimum Equiripple Linear-Phase FIR Filters

10.2.5 Design of FIR Differentiators

10.2.6 Design of Hilbert Transformers

10.2.7 Comparison of Design Methods for Linear-Phase FIR Filters

10.3 Design of IIR Filters From Analog Filters

10.3.1 IIR Filter Design by Approximation of Derivatives

10.3.2 IIR Filter Design by Impulse Invariance

10.3.3 IIR Filter Design by the Bilinear Transformation

10.3.4 Characteristics of Commonly Used Analog Filters

10.3.5 Some Examples of Digital Filter Designs Based on the Bilinear Transformation

10.4 Frequency Transformations

10.4.1 Frequency Transformations in the Analog Domain

10.4.2 Frequency Transformations in the Digital Domain

10.5 Summary

Problems

Computer Problems

**1****1****. ****Multirate Digital Signal Processing **11.1 Introduction

11.2 Decimation by a Factor D

11.3 Interpolation by a Factor I

11.4 Sampling Rate Conversion by a Rational Factor I /D

11.5 Implementation of Sampling Rate Conversion

11.5.1 Polyphase Filter Structures

11.5.2 Interchange of Filters and Downsamplers/Upsamplers

11.5.3 Sampling Rate Conversion with Cascaded Integrator Comb Filters

11.5.4 Polyphase Structures for Decimation and Interpolation Filters

11.5.5 Structures for Rational Sampling Rate Conversion

11.6 Multistage Implementation of Sampling Rate Conversion

11.7 Sampling Rate Conversion of Bandpass Signals

11.8 Sampling Rate Conversion by an Arbitrary Factor

11.8.1 Arbitrary Resampling with Polyphase Interpolators

11.8.2 Arbitrary Resampling with Farrow Filter Structures

11.9 Applications of Multirate Signal Processing

11.9.1 Design of Phase Shifters

11.9.2 Interfacing of Digital Systems with Different Sampling Rates

11.9.3 Implementation of Narrowband Lowpass Filters

11.9.4 Subband Coding of Speech Signals

11.10 Summary

Problems

Computer Problems

**12****. ****Multirate****Digital Filter Banks and Wavelets **12.1 Multirate Digital Filter Banks

12.1.1 DFT Filter Banks

12.1.2 Polyphase Structure of the Uniform DFT Filter Bank

12.1.3 An Alternative Structure of the Uniform DFT Filter Bank

12.2 Two-Channel Quadrature Mirror Filter Bank

12.2.1 Elimination of Aliasing

12.2.2 Polyphase Structure of the QMF Bank

12.2.3 Condition for Perfect Reconstruction

12.2.4 Linear Phase FIR QMF Bank

12.2.5 IIR QMF Bank

12.2.6 Perfect Reconstruction in Two-Channel FIR QMF Bank

12.2.7 Two-Channel Paraunitary QMF Bank

12.2.8 Orthogonal and Biorthogonal Two-channel FIR Filter Banks

12.2.9 Two-Channel QMF Banks in Subband Coding

12.3 M-Channel Filter Banks

12.3.1 Polyphase Structure for the M-Channel Filter Bank

12.3.2 M-Channel Paraunitary Filter Banks

12.4 Wavelets and Wavelet Transforms

12.4.1 Ideal Bandpass Wavelet Decomposition

12.4.2 Signal Spaces and Wavelets

12.4.3 Multiresolution Analysis and Wavelets

12.4.4 The Discrete Wavelet Transform

12.5 From Wavelets to Filter Banks

12.5.1 Dilation Equations

12.5.2 Orthogonality Conditions

12.5.3 Implications of Orthogonality and Dilation Equations

12.6 From Filter Banks to Wavelets

12.7 Regular Filters and Wavelets

12.8 Summary

Problems

Computer Problems

**13****. ****Linear Prediction and Optimum Linear Filters **13.1 Random Signals, Correlation Functions, and Power Spectra

13.1.1 Random Processes

13.1.2 Stationary Random Processes

13.1.3 Statistical (Ensemble) Averages

13.1.4 Statistical Averages for Joint Random Processes

13.1.5 Power Density Spectrum

13.1.6 Discrete-Time Random Signals

13.1.7 Time Averages for a Discrete-Time Random Process

13.1.8 Mean-Ergodic Process

13.1.9 Correlation-Ergodic Processes

13.1.10 Correlation Functions and Power Spectra for Random Input Signals to LTI Systems

13.2 Innovations Representation of a Stationary Random Process

13.2.1 Rational Power Spectra

13.2.2 Relationships Between the Filter Parameters and the Autocorrelation Sequence

13.3 Forward and Backward Linear Prediction

13.3.1 Forward Linear Prediction

13.3.2 Backward Linear Prediction

13.3.3 The Optimum Reflection Coefficients for the Lattice Forward and Backward Predictors

13.3.4 Relationship of an AR Process to Linear Prediction

13.4 Solution of the Normal Equations

13.4.1 The Levinson–Durbin Algorithm

13.5 Properties of the Linear Prediction-Error Filters

13.6 AR Lattice and ARMA Lattice-Ladder Filters

13.6.1 AR Lattice Structure

13.6.2 ARMA Processes and Lattice-Ladder Filters

13.7 Wiener Filters for Filtering and Prediction

13.7.1 FIR Wiener Filter

13.7.2 Orthogonality Principle in Linear Mean-Square Estimation

13.7.3 IIR Wiener Filter

13.7.4 Noncausal Wiener Filter

13.8 Summary

Problems

Computer Problems

**14****. ****Adaptive Filters **14.1 Applications of Adaptive Filters

14.1.1 System Identification or System Modeling

14.1.2 Adaptive Channel Equalization

14.1.3 Suppression of Narrowband Interference in a Wideband Signal

14.1.4 Adaptive Line Enhancer

14.1.5 Adaptive Noise Cancelling

14.1.6 Adaptive Arrays

14.2 Adaptive Direct-Form FIR Filters - The LMS Algorithm

14.2.1 Minimum Mean-Square-Error Criterion

14.2.2 The LMS Algorithm

14.2.3 Related Stochastic Gradient Algorithms

14.2.4 Properties of the LMS Algorithm

14.3 Adaptive Direct-Form Filters - RLS Algorithms

14.3.1 RLS Algorithm

14.3.2 The LDU Factorization and Square-Root Algorithms

14.3.3 Fast RLS Algorithms

14.3.4 Properties of the Direct-Form RLS Algorithms

14.4 Adaptive Lattice-Ladder Filters

14.4.1 Recursive Least-Squares Lattice-Ladder Algorithms

14.4.2 Other Lattice Algorithms

14.4.3 Properties of Lattice-Ladder Algorithms

14.5 Stability and Robustness of Adaptive Filter Algorithms

14.6 Summary

Problems

Computer Problems

**15****. ****Power Spectrum Estimation **15.1 Estimation of Spectra from Finite-Duration Observations of Signals

15.1.1 Computation of the Energy Density Spectrum

15.1.2 Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram

15.1.3 The Use of the DFT in Power Spectrum Estimation

15.2 Nonparametric Methods for Power Spectrum Estimation

15.2.1 The Bartlett Method: Averaging Periodograms

15.2.2 The Welch Method: Averaging Modified Periodograms

15.2.3 The Blackman and Tukey Method: Smoothing the Periodogram

15.2.4 Performance Characteristics of Nonparametric Power Spectrum Estimators

15.2.5 Computational Requirements of Nonparametric Power Spectrum Estimates

15.3 Parametric Methods for Power Spectrum Estimation

15.3.1 Relationships Between the Autocorrelation and the Model Parameters

15.3.2 The Yule–Walker Method for the AR Model Parameters

15.3.3 The Burg Method for the AR Model Parameters

15.3.4 Unconstrained Least-Squares Method for the AR Model Parameters

15.3.5 Sequential Estimation Methods for the AR Model Parameters

15.3.6 Selection of AR Model Order

15.3.7 MA Model for Power Spectrum Estimation

15.3.8 ARMA Model for Power Spectrum Estimation

15.3.9 Some Experimental Results

15.4 ARMA Model Parameter Estimation

15.5 Filter Bank Methods

15.5.1 Filter Bank Realization of the Periodogram

15.5.2 Minimum Variance Spectral Estimates

15.6 Eigenanalysis Algorithms for Spectrum Estimation

15.6.1 Pisarenko Harmonic Decomposition Method

15.6.2 Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in White Noise

15.6.3 MUSIC Algorithm

15.6.4 ESPRIT Algorithm

15.6.5 Order Selection Criteria

15.6.6 Experimental Results

15.7 Summary

Problems

Computer Problems

A. Random Number Generators

B.Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters

References and Bibliography

Answers to Selected Problems

Index

Published by Pearson (June 1st 2021) - Copyright © 2022